Insert at End of Doubly Linked List in DSA Java - Time & Space Complexity

Time Complexity: Insert at End of Doubly Linked List

O(1)

Understanding Time Complexity

We want to understand how the time to insert a new node at the end of a doubly linked list changes as the list grows.

How does the number of steps needed grow when the list gets longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public void insertAtEnd(int data) {
    Node newNode = new Node(data);
    if (head == null) {
        head = newNode;
        tail = newNode;
        return;
    }
    tail.next = newNode;
    newNode.prev = tail;
    tail = newNode;
}

This code adds a new node at the end of a doubly linked list by updating pointers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Updating pointers to add the new node at the end.
• How many times: This happens once per insertion, no loops or traversals.

How Execution Grows With Input

Since the code uses a tail pointer, it directly accesses the end without walking through the list.

Input Size (n)	Approx. Operations
10	5 steps (pointer updates)
100	5 steps (same as above)
1000	5 steps (still constant)

Pattern observation: The number of steps stays the same no matter how big the list is.

Final Time Complexity

Time Complexity: O(1)

This means inserting at the end takes the same amount of time regardless of list size.

Common Mistake

[X] Wrong: "Inserting at the end always takes longer as the list grows because we must walk through the list."

[OK] Correct: When we keep a tail pointer, we do not need to walk through the list; we directly access the end, so time stays constant.

Interview Connect

Knowing how to efficiently insert at the end of a doubly linked list shows you understand pointer management and how to keep operations fast as data grows.

Self-Check

"What if we did not keep a tail pointer and had to find the end each time? How would the time complexity change?"

Practice

1. What is the main purpose of inserting a node at the end of a doubly linked list?

easy

A. To reverse the list

B. To remove the first node

C. To add a new element after the last node

D. To find the middle node

Solution

1. Step 1: Understand the structure of a doubly linked list

   A doubly linked list has nodes connected both forward and backward, allowing traversal in both directions.

2. Step 2: Purpose of insertion at the end

   Inserting at the end means adding a new node after the current last node, updating pointers accordingly.

3. Final Answer:

   To add a new element after the last node -> Option C

4. Quick Check:

   Insert at end = Add after last node [OK]

Hint: Insert at end means add after last node [OK]

Common Mistakes:

• Confusing insertion at end with deletion
• Thinking insertion at end reverses the list
• Assuming insertion at end finds middle node

2. Which of the following is the correct way to update the 'next' pointer of the last node when inserting a new node at the end in Java?

easy

A. last.next = newNode;

B. newNode.next = last;

C. last.prev = newNode;

D. newNode.prev = null;

Solution

1. Step 1: Identify the last node's next pointer

   The last node's 'next' pointer should point to the new node being inserted.

2. Step 2: Correct assignment for insertion

   Assigning 'last.next = newNode;' correctly links the last node to the new node.

3. Final Answer:

   last.next = newNode; -> Option A

4. Quick Check:

   Last node's next points to new node [OK]

Hint: Last node's next must point to new node [OK]

Common Mistakes:

• Assigning newNode.next to last instead of last.next to newNode
• Changing last.prev instead of last.next
• Setting newNode.prev to null incorrectly

3. What will be the output of the following code snippet after inserting 40 at the end of the doubly linked list?

class Node {
  int data;
  Node next, prev;
  Node(int d) { data = d; next = prev = null; }
}

class DoublyLinkedList {
  Node head;
  void insertEnd(int data) {
    Node newNode = new Node(data);
    if (head == null) {
      head = newNode;
      return;
    }
    Node last = head;
    while (last.next != null) last = last.next;
    last.next = newNode;
    newNode.prev = last;
  }
  void printList() {
    Node temp = head;
    while (temp != null) {
      System.out.print(temp.data + " <-> ");
      temp = temp.next;
    }
    System.out.println("null");
  }
}

public class Main {
  public static void main(String[] args) {
    DoublyLinkedList dll = new DoublyLinkedList();
    dll.insertEnd(10);
    dll.insertEnd(20);
    dll.insertEnd(30);
    dll.insertEnd(40);
    dll.printList();
  }
}

medium

A. 10 <-> 20 <-> 30 <-> 40 <-> null

B. 40 <-> 10 <-> 20 <-> 30 <-> null

C. 10 <-> 20 <-> 30 <-> null

D. null

Solution

1. Step 1: Trace insertions in order

   Nodes 10, 20, 30, then 40 are inserted at the end, so list grows as 10 <-> 20 <-> 30 <-> 40.

2. Step 2: Print list traversal

   Print starts at head (10) and moves forward printing each node's data followed by ' <-> ', ending with 'null'.

3. Final Answer:

   10 <-> 20 <-> 30 <-> 40 <-> null -> Option A

4. Quick Check:

   Insertion at end appends nodes in order [OK]

Hint: Insertion order matches printed list [OK]

Common Mistakes:

• Assuming new node is added at start
• Forgetting to update newNode.prev
• Printing list incorrectly or missing null

4. Identify the error in the following insertEnd method for a doubly linked list:

void insertEnd(int data) {
  Node newNode = new Node(data);
  if (head == null) {
    head = newNode;
  } else {
    Node last = head;
    while (last.next != null) {
      last = last.next;
    }
    last.next = newNode;
    newNode.next = last;
  }
}

medium

A. last.next should be set to head

B. The while loop condition should be last.prev != null

C. head should be updated to newNode when list is empty

D. newNode.next should be set to null, not last

Solution

1. Step 1: Analyze pointer assignments after loop

   After finding last node, last.next is set to newNode correctly, but newNode.next is wrongly set to last (previous node).

2. Step 2: Correct pointer for newNode.next

   Since newNode is last, its next should be null, and newNode.prev should point to last.

3. Final Answer:

   newNode.next should be set to null, not last -> Option D

4. Quick Check:

   Last node's next = newNode; newNode.next = null [OK]

Hint: Last node's next points newNode; newNode.next is null [OK]

Common Mistakes:

• Setting newNode.next to last instead of null
• Not updating newNode.prev to last
• Incorrect loop condition in while

5. Given a doubly linked list with nodes 5 <-> 15 <-> 25, write the sequence of pointer updates needed to insert a new node with value 35 at the end. Which of the following correctly describes the steps?

hard

A. Set newNode.prev and newNode.next to null, head to newNode

B. Set newNode.prev to last node, last.next to newNode, newNode.next to null

C. Set newNode.next to last node, last.prev to newNode, newNode.prev to null

D. Set last.next to null, newNode.prev to null, newNode.next to last

Solution

1. Step 1: Identify last node and new node pointers

   The last node is 25; newNode is 35. For insertion at end, newNode.prev must point to last node, and last.next must point to newNode.

2. Step 2: Set newNode.next to null

   Since newNode is now last, its next pointer must be null to mark list end.

3. Final Answer:

   Set newNode.prev to last node, last.next to newNode, newNode.next to null -> Option B

4. Quick Check:

   Insert at end updates prev and next pointers correctly [OK]

Hint: New node prev = last; last next = new node; new node next = null [OK]

Common Mistakes:

• Swapping prev and next pointers incorrectly
• Not setting newNode.next to null
• Changing head pointer unnecessarily